Nonlinear Valley Hall Effect*

The energy minima of the electronic bands in the momentum space is referred to as valley. It is now considered a new degree of freedom which has led to the emergence of the field of valleytronics. 

The linear valley Hall effect (VHE), introduced by Di Xiao et al. enables electrical control and manipulation of the valley degree of freedom. VHE is the accumulation of electrons with opposite valley indices on opposite sides of a sample, transverse to the direction of the applied electric field. It is induced by the valley contrasting Berry curvature in materials with broken inversion symmetry.  However, in systems with inversion and time-reversal symmetry, the Berry curvature and the consequent VHE vanishes. This raises a fundamental question. Can we probe the valley degree of freedom in nonmagnetic and inversion symmetric materials? If so, then how can this be achieved?

In my talk, I will delve into these questions and introduce the nonlinear valley Hall effect (NVHE) that can probe the valley degree of freedom in inversion and time-reversal symmetric systems. I will explain the underlying physical picture of the phenomena and discuss how the NVHE can be used to investigate the quantum metric in systems with both fundamental symmetries. I will discuss its connection to the electric field-induced orbital magnetic moment, and comment on the experimental aspects of NVHE. Finally, I will discuss the intrinsic and extrinsic nature of the phenomena by considering specific examples of strained graphene.